Joseph Sultana

Conformal Weyl gravity and perihelion precession

Department of Physics, University of Malta, Msida, Malta(Received 1 August 2012; published 2 October 2012)We investigate the perihelion shift of planetary motion in conformal Weyl gravity using the metric ofthe static, spherically symmetric solution discovered by Mannheim and Kazanas [Astrophys. J. 342, 635(1989)]. To this end we employ a procedure similar to that used by Weinberg for the Schwarzschildsolution, which has also been used recently to study the solar system effects of the cosmological constant . We show that besides the general relativistic terms obtained earlier from the Schwarzschild–de Sittersolution, the expression for the perihelion shift includes a negative contribution which arises from thelinear term r in the metric. Using data for perihelion shift observations, we obtain constraints on thevalue of the constant similar to that obtained earlier using galactic rotational curves.

Luminosity Correlations for Gamma-Ray Bursts and Implications for Their Prompt and Afterglow Emission Mechanisms

We present the relation between the (z- and k-corrected) spectral lags, ?, for the standard Swift energy bands 50-100?keV and 100-200?keV and the peak isotropic luminosity, L iso (a relation reported first by Norris et?al.), for a subset of 12 long Swift gamma-ray bursts (GRBs) taken from a recent study of this relation by Ukwatta et?al. The chosen GRBs are also a subset of the Dainotti et?al. sample, a set of Swift GRBs of known redshift, employed in establishing a relation between the (GRB frame) luminosity, LX , of the shallow (or constant) flux portion of the typical X-Ray Telescope GRB-afterglow light curve and the (GRB frame) time of transition to the normal decay rate, T brk. We also present the LX -T brk relation using only the bursts common in the two samples. The two relations exhibit a significant degree of correlation (? = ?0.65 for the L iso-? and ? = ?0.88 for the LX -T brk relation) and have surprisingly similar best-fit power-law indices (?1.19 ? 0.17 for L iso-? and ?1.10 ? 0.03 for LX -T brk). Even more surprisingly, we noted that although ? and T brk represent different GRB time variables, it appears that the first relation (L iso-?) extrapolates into the second one for timescales ? T brk. This fact suggests that these two relations have a common origin, which we conjecture to be kinematic. This relation adds to the recently discovered relations between properties of the prompt and afterglow GRB phases, indicating a much more intimate relation between these two phases than hitherto considered.

Exact Static Cylindrical Solution to Conformal Weyl Gravity

We present the exact exterior solution for a static and neutral cylindrically symmetric source in locally conformal invariant Weyl gravity. As a special case the general relativity analogue still can be attained, however only as a sub-family of solutions. Our solution contains a linear term that would thus result in a potential that grows linearly over large distances. This may have implications for exotic astrophysical structures as well as matter fields on the extremely small scale.

Charged Cylindrical Black Holes in Conformal Gravity

Considering cylindrical topology, we present the static solution for a charged black hole in conformal gravity. We show that unlike the general relativistic case, there are two different solutions, both including a factor which gives rise to a linear term in the potential, which also features in the neutral case. This may have significant ramifications for particle trajectories.

Gravitomagnetic effects in conformal gravity

Gravitomagnetic effects are characterized by two phenomena: first, the geodetic effect which describes the precession of the spin of a gyroscope in a free orbit around a massive object, second, the Lense-Thirring effect which describes the precession of the orbital plane about a rotating source mass. We calculate both these effects in the fourth-order theory of conformal Weyl gravity for the test case of circular orbits. We show that for the geodetic effect a linear term arises which may be interesting for high radial orbits, whereas for the Lense-Thirring effect the additional term has a diminishing effect for most orbits. Circular orbits are also considered in general leading up to a generalization of Keplers third law.

Thermodynamic geodesics of a Reissner Nordström black hole

Starting from a Geometrothermodynamics metric for the space of thermodynamic equilibrium states in the mass representation, we use numerical techniques to analyse the thermodynamic geodesics of a supermassive Reissner Nordström black hole in isolation. Appropriate constraints are obtained by taking into account the processes of Hawking radiation and Schwinger pair-production. We model the black hole in line with the work of Hiscock and Weems (Phys Rev D 41:1142–1151, 1990). It can be deduced that the relation which the geodesics establish between the entropy S and electric charge Q of the black hole extremises changes in the black hole’s mass. Indeed, the expression for the entropy of an extremal black hole is an exact solution to the geodesic equation. We also find that in certain cases, the geodesics describe the evolution brought about by the constant emission of Hawking radiation and charged-particle pairs.

The

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universe and quintessence

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The Problem of Inertia in a Friedmann Universe

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